Linguistic Mathematical Morphology w-operators in Fuzzy Color Space

Abstract

Color is a very important visual feature used in computer vision and image processing. Compared with grayscale images, color images can provide richer information. However, the direct extension of grayscale image algorithms to color is not always straightforward. Usually, Mathematical Morphology (MM) is based on lattice theory; therefore, the most elementary requirement to define morphological color operators was thought to establish an ordering of the space of the pixel intensities. Several attempts have been made, and different approaches have been presented in the last years, aiming at building a fuzzy mathematical morphology model. The situation has become more complex when trying to apply fuzzy set theory in color images because of the existence of many different ordering schemes and different definitions for the basic morphological operators. The use of fuzzy set theory is appropriate to manage the imprecision in color description. Moreover, in practical applications, it is usual to work with different color terms, whose number and design depend on the application itself. In this sense, the concept of linguistic color space is useful, among other things, for representing the set of fuzzy colors that are relevant to a certain application. In this article, we propose a novel definition of linguistic w-operators of the mathematical color morphology using diffuse definitions of color spaces, based on the original idea of binary morphology without the need to establish a grid or an order. This innovative proposal allows to reduce the ambiguity in the color description and avoid false colors.